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Euclidean dynamics

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  • We study a general class of Euclidean algorithms which compute the greatest common divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various tools of analytic combinatorics: generating functions, Dirichlet series, Tauberian theorems, Perron's formula and quasi-powers theorems. Such dynamical analyses can be used to perform the average-case analysis of algorithms, but also (dynamical) analysis in distribution.
    Mathematics Subject Classification: Primary: 68Q25, 68W40, 37E05, 37C30, 11M41; Secondary: 47A.

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